Finite Group Databasebeta

← Group #342126

Character table — Group #342126

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444222444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-11-1-11-111-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11111-1-1-111-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-1-111-1-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-11111-1-111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1111-1-111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111111-1-1111-11-1-1-1-1-1-111-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-11111111-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1111111-1-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-111-1-111-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-11-1-1-111111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-1-1-1-11-1-1-1-1-1111111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-111-11111-1-111-1-111-1-1
χ17222222222-2-22-2-222-2-2000000002222-2-2-2-20000000000002222-2000000-20000000000
χ18222222222-2-22-2-222-2-2000000002222-2-2-2-2000000000000-2-2-2-2200000020000000000
χ19222222222-2-22-2-222-2-200000000-2-2-2-2222200000000000022-2-2-200000020000000000
χ20222222222-2-22-2-222-2-200000000-2-2-2-22222000000000000-2-2222000000-20000000000
χ2122222222-222-222-2-2-2-22222-2-2-2-2000000000000000022220000000-200-200000000000
χ2222222222-222-222-2-2-2-22222-2-2-2-20000000000000000-2-2-2-20000000200200000000000
χ2322222222-222-222-2-2-2-2-2-2-2-22222000000000000000022-2-20000000-200200000000000
χ2422222222-222-222-2-2-2-2-2-2-2-222220000000000000000-2-2220000000200-200000000000
χ2522-22-22-2-202-202-200002i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i22222−2−2−2−22-22i−2i0000000000002−20000i2−i200
χ2622-22-22-2-202-202-200002i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i22222−2−2−2−2-22−2i2i000000000000−220000−i2i200
χ2722-22-22-2-202-202-200002i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i2−2−2−2−222222-22i−2i000000000000−220000−i2i200
χ2822-22-22-2-202-202-200002i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i2−2−2−2−22222-22−2i2i0000000000002−20000i2−i200
χ2922-22-22-2-202-202-20000−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i2−2−2−2−222222-2−2i2i000000000000−220000i2−i200
χ3022-22-22-2-202-202-20000−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i2−2−2−2−22222-222i−2i0000000000002−20000−i2i200
χ3122-22-22-2-202-202-20000−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i22222−2−2−2−22-2−2i2i0000000000002−20000−i2i200
χ3222-22-22-2-202-202-20000−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i22222−2−2−2−2-222i−2i000000000000−220000i2−i200
χ332-2-222-2-22200200-2-2002−22−222−2−22-22-2000022−2−222−2−200002i−2i2i−2i0000000000i2−i2i2−i20000
χ342-2-222-2-22200200-2-2002−22−222−2−22-22-2000022−2−222−2−20000−2i2i−2i2i0000000000−i2i2−i2i20000
χ352-2-222-2-22200200-2-2002−22−222−2−2-22-220000−2−222−2−22200002i−2i−2i2i0000000000i2−i2−i2i20000
χ362-2-222-2-22200200-2-2002−22−222−2−2-22-220000−2−222−2−2220000−2i2i2i−2i0000000000−i2i2i2−i20000
χ372-2-222-2-22200200-2-200−22−22−2−2222-22-20000−2−222−2−22200002i−2i2i−2i0000000000−i2i2−i2i20000
χ382-2-222-2-22200200-2-200−22−22−2−2222-22-20000−2−222−2−2220000−2i2i−2i2i0000000000i2−i2i2−i20000
χ392-2-222-2-22200200-2-200−22−22−2−222-22-22000022−2−222−2−200002i−2i−2i2i0000000000−i2i2i2−i20000
χ402-2-222-2-22200200-2-200−22−22−2−222-22-22000022−2−222−2−20000−2i2i2i−2i0000000000i2−i2−i2i20000
χ412-2-2-2-2222222-2-2-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i0000000002-202i−2i000000000000
χ422-2-2-2-2222222-2-2-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000-220−2i2i000000000000
χ432-2-2-2-2222222-2-2-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000002-20−2i2i000000000000
χ442-2-2-2-2222222-2-2-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000-2202i−2i000000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-4-44400-400-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ47444-4-4-4-44400-400-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ48444-4-4-4-44-4004004-4000000000000004i−4i4i−4i0000000000000000000000000000000000
χ49444-4-4-4-44-4004004-400000000000000−4i4i−4i4i0000000000000000000000000000000000
χ5044-44-44-4-40-440-440000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ5144-44-44-4-40-440-44000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ5244-4-44-44-4000000000000002i2−2i22i2−2i2000022−22−22222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5344-4-44-44-4000000000000002i2−2i22i2−2i20000−222222−22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5444-4-44-44-400000000000000−2i22i2−2i22i2000022−22−2222−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5544-4-44-44-400000000000000−2i22i2−2i22i20000−222222−222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ564-444-4-44-400000000002i2−2i2−2i22i200002i2−2i2−2i22i2000022-2-2-2-22200000000000000000000000000
χ574-444-4-44-400000000002i2−2i2−2i22i20000−2i22i22i2−2i20000-2-22222-2-200000000000000000000000000
χ584-444-4-44-40000000000−2i22i22i2−2i200002i2−2i2−2i22i20000-2-22222-2-200000000000000000000000000
χ594-444-4-44-40000000000−2i22i22i2−2i20000−2i22i22i2−2i2000022-2-2-2-22200000000000000000000000000
χ604-44-444-4-404-40-44000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ614-44-444-4-404-40-4400000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ624-44-444-4-40-4404-4000000004i−4i−4i4i000000000000000000000000000000000000000000
χ634-44-444-4-40-4404-400000000−4i4i4i−4i000000000000000000000000000000000000000000
χ644-4-444-4-44-400-400440022−2222−22−22−222222000000000000000000000000000000000000000000
χ654-4-444-4-44-400-4004400−2222−22222222−22−22000000000000000000000000000000000000000000
χ664-4-4-4-44444-4-4-4444-4-4400000000000000000000000000000000000000000000000000
χ674-4-4-4-4444-4444-4-4-44-4400000000000000000000000000000000000000000000000000
χ684-4-4-4-4444-4-4-4444-444-400000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).